Certainly! Let's walk through the step-by-step solution to determine how many moles of sodium hydroxide (NaOH) will be produced from the complete reaction of 15.0 grams of sodium (Na).
Step 1: Identify the given values.
- Mass of sodium (Na): 15.0 grams.
- Molar mass of sodium (Na): 22.99 grams per mole (g/mol).
Step 2: Calculate the number of moles of sodium ([tex]\( \text{Na} \)[/tex]).
To find the number of moles, we use the formula:
[tex]\[
\text{moles of Na} = \frac{\text{mass of Na}}{\text{molar mass of Na}}
\][/tex]
Substituting in the given values:
[tex]\[
\text{moles of Na} = \frac{15.0 \, \text{grams}}{22.99 \, \text{g/mol}}
\][/tex]
Step 3: Use the stoichiometry of the balanced chemical equation.
The balanced equation is:
[tex]\[
2\text{Na} + 2\text{H}_2\text{O} \rightarrow 2\text{NaOH} + \text{H}_2
\][/tex]
According to the balanced equation, 2 moles of Na produce 2 moles of NaOH, indicating a 1:1 mole ratio between Na and NaOH.
Step 4: Determine the moles of NaOH produced.
Since the ratio is 1:1:
[tex]\[
\text{moles of NaOH} = \text{moles of Na}
\][/tex]
Therefore:
The number of moles of sodium:
[tex]\[
\text{moles of Na} = 0.6524575902566334
\][/tex]
Given the 1:1 mole ratio, the moles of sodium hydroxide produced will also be:
[tex]\[
\text{moles of NaOH} = 0.6524575902566334
\][/tex]
Hence, the complete reaction of 15.0 grams of sodium will produce approximately 0.652 moles of sodium hydroxide ([tex]\( \text{NaOH} \)[/tex]).
